Both sides were chasing an Easter double after beating Wigan and Fulham respectively on Good Friday and both were looking to open up a gap on each other
However, the three points remained out of reach as did the chance to close the gap on faltering Arsenal.
The match had been billed as a show down between strikers Nicolas Anelka and Andrew Johnson. Wanderers splashed out £8million on Anelka after failing to land Johnson from Crystal Palace.
In the end though, it was their second in commands who grabbed the goal headlines.
Bolton made the best possible start with Kevin Davies giving Sam Allardyce's team an 18th minute lead.
Davies, who scored a late winner against Sheffield United last weekend, netted his seventh of the season.
Ivan Campo, restored to the side after a two-game suspension, floated in a free-kick, Everton's offside trap failed dismally and Davies volleyed home past Tim Howard.
However, Everton are also running into some late season form and they were level 12 minutes before half-time.
Teenager James Vaughan is keeping £6million misfit James Beattie out of the team. And the 18-year-old prospect showed the reason why with his second goal in as many games - his third of the campaign.
Leon Osman was involved in the build-up and it was his pass that Vaughan turned in from six yards to level the scores.
But Vaughan's day had an unhappy ending, when he was stretchered off on the hour mark with an ankle injury.
Joseph Yobo almost snatched victory for the visitors after a goalmouth melee.
However, Bolton's defenders did their jobs and the match eventually petered out into a creditable draw.
Allardyce's side now visits Arsenal on Saturday in a match that could determine who snatches fourth spot at the end of the season.